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Preprint 5-2012

Properties of the interface of the symbiotic branching model

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Author(s) : Jochen Blath , Marcel Ortgiese

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 5-2012

MSC 2000

60K35 Interacting random processes; statistical mechanics type models; percolation theory
60J80 Branching processes

Abstract :
The symbiotic branching model describes the evolution of two interacting populations and if started with complementary Heaviside functions, the interface where both populations are present remains compact. In this paper, we show tightness of the diffusively rescaled solutions and thus provide a rst step towards a scaling limit for the interface. The crucial estimate involves a mixed fourth moment bound which we analyse using a particle system duality. As a corollary, we obtain an estimate on the moments of the width of an approximate interface.

Keywords : Symbiotic branching model, mutually catalytic branching, stepping stone model, propagation of interface, moment duality.

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